On 5 January 2011, during his sophomore NHL season in 2010–11, Hedman checked Pittsburgh Penguins captain Sidney Crosby from behind, receiving a minor boarding penalty. The hit was one of two that were eventually blamed for causing a severe concussion on Crosby that kept him out of play for over a year.[6][7]

On 29 November 2011, shortly into the 2011–12 season, Hedman signed a five-year, $20 million contract extension with Tampa Bay. On 25 September 2012, it was announced that Hedman signed a contract with Barys Astana of the KHL during the 2012–13 NHL lockout. During the 2013–14 season, Hedman had a breakout season, posting a career best in goals (13), assists (42) and points (55).

Hedman followed up his breakout season with a strong start to the 2014–15 season. However, his start would be derailed after he suffered a broken finger, which was expected to rule him out of play for four to six weeks. At the time, Hedman was tied for the lead amongst NHL defencemen with seven points, and was considered a possible James Norris Memorial Trophy candidate for Defenceman of the Year entering into the season.[8] Despite the injury, Hedman still had a productive season with the Lightning, scoring 10 goals, 28 assists and 38 points in 59 games played. After Game 2 of the Stanley Cup Final against the Chicago Blackhawks, Hedman had recorded the most points by a Lightning defencemen in a single playoff year, with one goal, 11 assists and 12 points.[9] On 8 June 2015, during Game 3 of the Final series, Hedman set Lightning records for career playoff assists (20) and points (23) by a defenceman, surpassing Dan Boyle, who previously held the record with three goals and 19 assists (22 points).[10]

On 24 October 2015, Hedman played in his 400th career NHL game in an OT loss to the Chicago Blackhawks.[11] On 20 December 2015, Hedman recorded his 200th NHL point, which was an assist on a Nikita Kucherov power play goal. The point came during a 5–2 Lightning victory over the visiting Ottawa Senators.[12] On 20 May 2016, Hedman recorded two assists in a 4–3 Lightning win over the Pittsburgh Penguins. The two assists moved Hedman past Vincent Lecavalier (28) and Brad Richards (29) for number two all-time in playoff assists with the franchise.[13] On 24 May 2016, Hedman became the leader in playoff games played for the Lightning. He surpassed former teammates Martin St. Louis and Vincent Lecavalier, who were tied for the most playoffs games played in franchise history.[14]

On July 1, 2016, the Lightning re-signed Hedman to an eight-year contract extension worth $7.875 million per season. Hedman lead all Lightning defensemen in goals, assists (37), points and plus/minus. He also led all Lightning skaters in plus/minus, average ice time (23:03), takeaways (48) and blocked shots (132). He also posted a career high with a plus-21 rating. Hedman currently ranks third all-time in franchise history among defensemen in career points (229), behind Dan Boyle (253) and Pavel Kubina (243). He is also second all-time among defensemen in assists (180) and fourth for goals (49). Hedman ranks third all-time among Lightning defensemen for games played, trailing only Pavel Kubina (662) and Cory Sarich (490). In addition, Hedman is the Bolts' all-time playoff leader for points, goals, assists and plus/minus among defensemen.[15]

Hedman in September 2011

On October 26, 2016, Hedman recorded his 50th career NHL goal.[16] The goal came in a 7-3 Lightning victory over the Toronto Maple Leafs at the Air Canada Centre.[17] On November 5, 2016, Hedman recorded his 187th assist, which tied him with Dan Boyle for most career assists by a Lightning defenseman.[18] The assist came in a 4-1 Lightning victory over the visiting New Jersey Devils.[19] On November 10, 2016, Hedman recorded his 188th career assist which is the most assists by a defenseman in Lightning history.[20] Hedman is now seventh in franchise history in assists.[21] On November 14, 2016, Hedman recorded his 189th assist, which tied with Brian Bradley for 6th in assists in Lightning history. The assist came in a 4-0 Lightning win over the New York Islanders at the Barclays Center.[22] On November 15, 2016, Hedman recorded his 190th assist, which moved Hedman past Bradley for sixth all time in assists in Lightning history. The assist came in a 4-3 win over the Detroit Red Wings at Joe Louis Arena.[23] On November 21, 2016, Hedman recorded an assist, which was Hedman's 243rd career point. This put Hedman into a tie with Pavel Kubina for 10th place on the Lightning's all-time scoring list.[24] Hedman is also tied with Kubina for 2nd all-time in points by a defensemen in Lightning history. On November 23, 2016, Hedman recorded a goal in a 4-2 Lightning victory over the visiting Philadelphia Flyers. This was Hedman's 244th career point, which moved him past Kubina for 2nd in points by a defenseman and 10th in points in Lightning history.[25]

On December 14, 2016, Hedman skated in his 500th career NHL game, which came in a 6-3 Lightning victory over the Calgary Flames. Additionally, Hedman recorded three assists, and now only needs two points to tie Dan Boyle (253) for most all-time points by a Lightning defenseman.[26] On December 16, 2016, Heman recorded his 253rd career NHL point, which moved him into a tie with Dan Boyle.[27] On December 17, 2016, Hedman became the all-time leader in points by a defenseman with his 254th career point. Hedman also moved into 9th place on the all-time franchise list for all skaters.[28] On December 20, 2016, Hedman recorded his 200th career NHL assist.[29] Hedman also became the first defensemen in Lightning history to record 200 career assists.[30] On December 28, 2016, Hedman recorded two points to move past Chris Gratton in to eighth place on the Lightning's all-time scoring list.[31] On January 10, 2017, Hedman was named to the 2017 NHL All-Star game as a member of the Atlantic Division team.[32] On February 23, 2017, Hedman recorded his 526th and 527th career hits against the Calgary Flames, which moved him past Eric Brewer for the most hits in Lightning history.[33][34] On March 11, 2017, Hedman recorded his 287th career point in a Lightning uniform. This moved him past Fredrik Modin for 7th most points all-time in franchise history.[35] On March 27, 2017, Hedman recorded his 50th assist of the season to become the first defenseman in Lightning history to record 50th assists in a single season.[36] On March 30, 2017, Hedman recorded an assist in the second period to move him past Roman Hamrlik for the most points (66) in a single season by a defenseman in Lightning history.[37] On April 6, 2017, Hedman recorded three assists to become the first defenseman in Lightning history to reach 70-points in a single season.[38] Hedman also joined Börje Salming, Nicklas Lidström, and Erik Karlsson as the only Swedish defensemen to reach 70-points in a single season.[39] On April 9, 2017, Hedman recorded a goal and an assist in a 4-2 Lightning win over the visiting Buffalo Sabres.[40] Hedman's two points moved him past Brian Bradley for sixth all-time in franchise history in points (301).[41] On April 21, 2017, Hedman was named as a finalist for the James Norris Memorial Trophy, which is awarded annually to the NHL's top defenseman.[42] Hedman finished third in Norris voting that season.[43] On June 21, 2017, Hedman was named as a NHL Second Team All Star for the 2016-17 season.[44]

On October 12, 2017, Hedman skated in his 553rd game, which moved Hedman past Brad Richards for fifth most games played in Lightning history.[45] On the same night, Hedman recorded his 66th goal in his career. This goal moved him into a tie with Dan Boyle for 2nd most goals by a Lightning defensemen in franchise history.[46] On November 4, 2017, Hedman recorded two assists in a 5-4 Lightning win over the visiting Columbus Blue Jackets.[47] The two assists moved Hedman past Václav Prospal (245) for 5th most assists in Lightning franchise history.[48] On January 10, 2018, Hedman was named to the 2018 NHL All-Star Game.[49] Hedman also became the only defenseman in Lightning history to be named to multiple All-Star games.[50] However, he could not play due to injury and he was replcaed by Brayden Point.[51] Hedman was unable to play in the All-Star game due to an injury suffered prior to the event. However, Hedman did participate in the event by serving an assistant equipment manager.[52] On February 8, 2018, Hedman recorded a goal in a 5-2 win over the visiting Vancouver Canucks. The goal moved Hedman past Pavel Kubina for the most goals by a defenseman in franchise history.[53]

On April 15, 2017, the Swedish Ice Hockey Association named Hedman to its roster for the 2017 IIHF World Championship.[56] On April 28, 2017, Hedman was named as an assistant captain for the tournament.[57] On May 21, 2017, Hedman helped team Sweden capture gold in a 2-1 victory over Canada.[58]

Hedman has two older brothers — Oscar Hedman, who is also a professional hockey player that currently plays for Modo Hockey; as well as Johan Hedman, who does not play professionally.

As a child, Hedman originally started out playing as a goaltender. His father, Olle Hedman, told his son that if he left the net, he would purchase him the new helmet that he coveted. He has not played in goal since that day. Victor said "I'm thankful for that now. You never know what would have happened otherwise."[59]

Hedman's other passions were flying (he has logged eight hours on a Piper PA-32), and soccer. His father said that his son would just outrun everyone on the field. Hedman still plays soccer in the summer, and religiously follows the sport. In an article it was revealed that when quizzed on any player on any English Premier League team, he couldn't be stumped. His dad said that his son "probably knows more about football than hockey. However, Hedman knew that hockey was his future. He was encouraged by some of hockey's greats. The players would come back every summer and play for a team called the Icebreakers, inviting Hedman to play. Some notable players on the team included Peter Forsberg, Markus Näslund, Henrik Zetterberg, and Nicklas Bäckström. Hedman said that "looking back at it now, it was an unbelievable experience."[60]

In 2014 Hedman started a hockey school in his hometown. The spots in the school sold out in two hours. Hedman said that "to see the thrill in the kids' eyes, it's worth it all."[61]

During an interview with The Hockey News, Hedman revealed why he chose No. 77 as his jersey number. Hedman revealed that Nicklas Lidström was an idol of his growing up, however, he stated that he did not play the same style of game. Hedman said he liked the way Ray Bourque played the game. As well as guys like Paul Coffey due to their skating ability. Due to watching a lot of the Colorado Avalanche Hedman witnessed Bourque winning a cup with Colorado. Hedman wore No. 41 back in Sweden, but Lightning teammate Mike Smith wore that number. He decided to wear Bourque's No. 77 instead.[63] On July 23, 2017, Hedman married Sanna Grundberg.